When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is

Given,

Two dice are thrown in which we get prime number on one dice and composite number on other,

So possible outcomes will be $\left\{\left(2,4\right),\left(2,6\right),\left(3,4\right),\left(3,6\right),\left(5,4\right),\left(5,6\right),\left(4,2\right),\left(6,2\right),\left(4,3\right),\left(6,3\right),\left(4,5\right),\left(6,5\right)\right\}\to 12$

And total possible outcomes will be $6\times 6=36$

Now probability is given by $\frac{12}{36}=\frac{1}{3}$